In a pipe saddle disclosed in U.S. Pat. No. 3,582,029 to Moesta, the inwardly bent support part is of identical overall axial length about the recess. The axial length corresponds to approximately 1/4 to 1/5 of the distance between the two side pieces. With the saddle halves arranged at some spacing from each other, an elastic insert surrounding the pipe, the hose or the like is supported upright in such a manner that the insert middle section, located inside the pipe saddle, is curved outwardly upon tightening such that a tighter insert seat is attained. However, the specific surface pressure is not uniformly distributed.